What is the integral of ((ln(x)+1)^2)/x ?

The integral of ((ln(x)+1)^2)/x is ((ln(x)+1)^3)/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((ln(x)+1)^2)/x

\int \frac{( ln ( x ) + 1 ) ^{2}}{x} d x

\frac{( ln ( x ) + 1 ) ^{3}}{3} + C

Solution steps

\int \frac{( ln ( x ) + 1 ) ^{2}}{x} d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = ln (x) + 1

= \frac{( ln ( x ) + 1 ) ^{3}}{3}

Add a constant to the solution

= \frac{( ln ( x ) + 1 ) ^{3}}{3} + C

\int \frac{4 + 3 x ^{2}}{x ^{3} + 4 x} d x

\int 2 x 3 - 2 x^{2} d x

\int - 5 x + 10 - e^{- x} d x

\int (1 + sin^{2} (θ) csc (θ)) d θ

\int \frac{x ^{3}}{x ^{2} + 22 x + 121} d x

What is the integral of ((ln(x)+1)^2)/x ?
The integral of ((ln(x)+1)^2)/x is ((ln(x)+1)^3)/3+C